Heretofore it has been well known to play a variety of different games with a standard deck of fifty-two playing cards, including Blackjack, Poker, Bridge, Gin Rummy, etc. Games such as Blackjack are universally played in casinos and other such establishments because each player plays against the dealer or house and because they provide an edge to the dealer or house. Likewise, video draw poker machines in which a player individually plays against the house are widely found in casinos. In the video draw poker games there is an advantage to the house because the player needs a hand having a pair of Jacks or better to win. Other poker games, such as Seven-Card Stud, are not generally played in casinos because the rules of Poker require players to play against each other instead of each player playing against a single dealer or the house. The casinos are thus unable to profit from running such games. Moreover, in most poker games each player has one hand even though some variations allow the players to share certain cards. This limits the excitement of such games especially when a player initially receives a poor hand. In one known poker game, a draw poker machine gives the player two initial hands from two separate decks, and the player must select one of those hands to play while the other hand is discarded. U.S. Pat. No. 5,356,140 illustrates this game. While this game allows the player to select or play from one of two hands, it does not maintain the other hand in the game, and it does not allow another player to select the other hand. Accordingly, there is a need for an exciting poker-like game in which each player plays against the dealer or the house and in which each player can select his hand or a position after seeing a predetermined number of cards dealt to each hand.